A generalized expansion method for nonlinear wave equations

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 4, 2009, Pages

  Lin, Qun ^a   Wu, Yong Hong ^a   Loxton, Ryan ^a  

^a CURTIN UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64549129883     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/4/045207     Document Type: Article

References (23)

1. Abramowitz M and Stegun I A 1972 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Washington, DC: National Bureau of Standards) (tenth printing)
2. Chen Y and Wang Q 2006 A new elliptic equation rational expansion method and its application to the shallow long wave approximate equations Appl. Math. Comput. 173 1163-82
3. El-Sabbagh M F and Ali A T 2008 New generalized Jacobi elliptic function expansion method Commun. Nonlinear Sci. Numer. Simul. 13 1758-66
4. Fan E 2002 Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method J. Phys. A: Math. Gen. 35 6853-72
5. Gradshteyn I S and Ryzhik I M 1980 Table of Integrals, Series, and Products (San Diego, CA: Academic)
6. He J H and Wu X H 2006 Exp-function method for nonlinear wave equations Chaos Solitons Fractals 30 700-8
7. Lai S and Wu Y H 2003 The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation Discrete Continuous Dyn. Syst. Ser. B 3 401-8
8. Lai S, Wu Y H and Yang X 2004 The global solution of an initial boundary value problem for the damped Boussinesq equation Commun. Pure Appl. Anal. 3 319-28
9. Lai S, Wu Y H and Wiwatanapataphee B 2008 On exact travelling wave solutions for two types of nonlinear K(n, n) equations and a generalized KP equation J. Comput. Appl. Math. 212 291-9
10. Lai S, Wu Y H and Zhou Y 2008 Some physical structures for the (2 + 1)-dimensional Boussinesq water equation with positive and negative exponents Comput. Math. Appl. 56 339-45
11. Lin Q, Wu Y H, Loxton R and Lai S 2008 Linear B-spline finite element method for the improved Boussinesq equation J. Comput. Appl. Math. (doi:10.1016/j.cam.2008.05.049)
12. Liu S, Fu Z, Liu S and Zhao Q 2001 Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations Phys. Lett. A 289 69-74
13. Liu J, Yang L and Yang K 2004 Nonlinear transformation and Jacobi elliptic function solutions of nonlinear equations Chaos Solitons Fractals 20 1157-64
14. Lv X, Lai S and Wu Y H 2007 An auxiliary equation technique and exact solutions for a nonlinear Klein-Gordon equation Chaos Solitons Fractals (doi:10.1016/j.chaos.2007.11.013)
15. Malfliet W 1996 The tanh method: I. Exact solutions of nonlinear evolution and wave equations Phys. Scr. 54 563-8
16. Malfliet W 2004 The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations J. Comput. Appl. Math. 164-165 529-41
17. Nickel J 2007 Elliptic solutions to a generalized BBM equation Phys. Lett. A 364 221-6
18. Shen S and Pan Z 2003 A note on the Jacobi elliptic function expansion method Phys. Lett. A 308 143-8
19. Wazwaz A 2006 New hyperbolic schemes for reliable treatment of Boussinesq equation Phys. Lett. A 358 409-13
20. Wu X H and He J H 2007 Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method Comput. Math. Appl. 54 966-86
21. Yan Z 2003 Jacobi elliptic function solutions of nonlinear wave equations via the new sinh-Gordon equation expansion method J. Phys. A 36 1961-72
22. Zhang H 2007 Extended Jacobi elliptic function expansion method and its applications Commun. Nonlinear Sci. Numer. Simul. 12 627-35
23. Zhang H 2007 New exact Jacobi elliptic function solutions for some nonlinear evolution equations Chaos Solitons Fractals 32 653-60